Answer
$x=-1\pm\sqrt 2, \frac{2}{3}$
Work Step by Step
Step 1. List the possible rational solutions as
$\frac{p}{q}=\pm1,\pm2,\pm\frac{1}{3},\pm\frac{2}{3}$
Step 2. Using synthetic division to test solutions, we can find that $x=\frac{2}{3}$ is a zero as shown in the figure.
Step 3. The quotient can be found as $3x^2+6x-3=3(x^2+2x-1)=0$, which gives $x=\frac{-2\pm\sqrt {8}}{2}=-1\pm\sqrt 2$
Step 4. The solutions are $x=-1\pm\sqrt 2, \frac{2}{3}$
